Even Educators Don’t Understand Transfer

Two months ago Harry Webb wrote a post about “attempts to educate teachers” that included a brief discussion of How People Learn, the National Research Council’s attempt to condense a vast research literature on learning for classroom use.

I was reminded of my experience of reading HPL in grad school and wanted to write something in response, but wanted to find a particular passage from the book first and so bookmarked Harry’s post while I snooped around my apartment looking for my copy. As it turns out, I seem not to have it anymore, so the post collected dust in my “saved” Feedly items.

That turned out to be pretty daft on my part because – as I recently realized in a blinding-but-belated flash of insight – HPL is available in its entirety online. In fact, Harry’d even linked to it.

Why that fact eluded me for so long I will never know, but in any case the entire book is here (or here), and now I can say what I’d wanted to say.

Anyway, one of my most memorable experiences in my two-year credential+MA program came out of a class discussion of chapter 3 of How People Learn, on “Learning and Transfer”. Much of that chapter was dedicated to discussing the challenges faced in getting students to “transfer” something they’ve learned in one context and apply it successfully in another context (e.g., to a substantively similar but superficially different problem in the future).

To their credit, the authors of the book acknowledge that successful transfer to even moderately different problem contexts is extremely difficult. In fact, at one point in the chapter they dedicate an entire page to an aside about a study in 1980 illustrating the problem. From How People Learn:

College students were presented with the following passage about a general and a fortress (Gick and Holyoak, 1980:309).

A general wishes to capture a fortress located in the center of a country. There are many roads radiating outward from the fortress. All have been mined so that while small groups of men can pass over the roads safely, a large force will detonate the mines. A full-scale direct attack is therefore impossible. The general’s solution is to divide his army into small groups, send each group to the head of a different road, and have the groups converge simultaneously on the fortress.

Students memorized the information in the passage and were then asked to try another task, which was to solve the following problem (Gick and Holyoak, 1980:307– 308).

You are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that may be used to destroy the tumor. If the rays reach the tumor all at once and with sufficiently high intensity, the tumor will be destroyed, but surrounding tissue may be damaged as well. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and at the same time avoid destroying the healthy tissue?

Few college students were able to solve this problem when left to their own devices. However, over 90 percent were able to solve the tumor problem when they were explicitly told to use information about the general and the fortress to help them. These students perceived the analogy between dividing the troops into small units and using a number of small-dose rays that each converge on the same point—the cancerous tissue. Each ray is too weak to harm tissue except at the point of convergence. Despite the relevance of the fortress problem to the tumor problem, the information was not used spontaneously—the connection between the two sets of information had to be explicitly pointed out.

It’s hard to overstate the educational importance of this sort of lack of transfer. When we think of the educational ideal, we often imagine something very much like what the researchers attempted to do in this experiment. Students were taught a valuable problem-solving strategy – in this case, disperse the dangerous force across multiple entry roots such that they converge only on the desired target – and then asked to apply that very same strategy to a substantively similar problem.

And they couldn’t do it.

It’s a devastating finding. HPL’s authors try to sugar-coat it by subsequently introducing strategies teachers can use to marginally improve transfer, but the bottom line is a brutal one for educators who want students to be able to consistently take what they learn in the classroom and apply it in novel settings in the “real world”.

When I was in graduate school, we spent a good chunk of class time one day discussing that very passage. And everyone found it troubling, but for all the wrong reasons.

If you are an educator who strives primarily to help students achieve substantial transfer of abstract critical thinking and problem solving abilities, the Gick & Holyoak study should be philosophically troubling. After all, the study – and others like it – suggest very strongly that the sort of transfer many teachers claim to want is at best much more difficult than we typically acknowledge and at worst largely impossible.

That was not, however, the response in my graduate school classroom. There, the future teachers (including me) and educational researchers were intellectually troubled. Rather than challenging our conceptions of transfer, the finding simply represented a puzzle: Why did students not transfer the problem-solving strategy from one situation to the other and how could teachers have taught the strategy differently to promote such transfer?

My own understanding of transfer was still naive at the time, so I was mostly caught up in the “puzzle” as well. But in retrospect, there’s not really much of a puzzle at all.

There’s no puzzle because the students in the study clearly do understand the “dispersal/convergence” strategy. They understand it in the context of the invading army and they are perfectly able to apply it to the cancer-fighting rays when told to apply it.

If you already understand exactly how to apply the “dispersal/convergence” strategy to both problems, there’s a tendency to assume that someone who doesn’t spontaneously apply it in both contexts doesn’t “really” understand it. But this is our expertise blinding us to what’s really going on.

In reality, the only question is why the students don’t spontaneously apply the strategy to the tumor problem. And that is much less puzzling: they don’t spontaneously apply the strategy because they do not know that it applies usefully. They understand the strategy. What they don’t understand is the context: tumors, rays, etc.

In other words, the question isn’t “How should teachers present the strategies more effectively?” so much as “How should teachers present additional contexts more effectively?”

Notably and memorably, however, my graduate-level(!) discussion centered almost entirely around the former, largely intractable, mostly misguided question; the latter, more central question mostly escaped our notice. This was perhaps because How People Learn itself tends to promote the same confused interpretation of the “transfer problem”.

To circle briefly back to Harry’s original post, what are the implications of this sort of self-perpetuating educational confusion for the professional development of teachers?

As Harry says, some teachers will often have the wisdom to be “difficult” and just ignore the most unreasonable prescriptions of even supposedly reputable educational authorities. Certainly, you see some of this with a lot of “inquiry science“, which is as widely rejected in practice as it is praised in theory.

16 Comments

The ability to transfer problem-solving strategies to new contexts is also developmental, in my opinion. Trying to elicit it when the students are too young, or are not well-enough versed in the content that’s at hand, or when they are under the gun to master difficult content, will result in failure. Note: transferring a problem-solving strategy from one domain to another may worsen that difficulty. Military strategy is not very closely related to radiation physics.

Modern educational theory tends to fixate on “critical thinking” abilities and skills that you hope for as an outcome to a solid education, and try to elicit them in children who are not ready to operate at that level.

That might be. I tend to be suspicious of “developmentally inappropriate” arguments because 1) kids might be at different points developmentally and 2) any particular learning goal might appear developmentally inappropriate right up until the moment it doesn’t (i.e., when we figure out kids can handle it if presented in such-and-such a way.)

But it’s hard to say, and in any case the example I cited above is for college students, and presumably they’re “developmentally ready” for whatever it is we want them to learn.

This reminds me of our discussion about the term “creativity” a couple of years ago. When I use the term “creative,” I’m thinking of transfer. When I suggested, over our warm beverages at Rooz, that we needed to teach creativity, I was suggesting that we needed to explicitly teach this kind of transfer as an academic strategy.

I remember that conversation. Unfortunately, I don’t think there’s much evidence it would do much good. With these sorts of abstract strategies you can sometimes get a modest, one-time boost – especially with younger students who haven’t yet developed the strategy independently – but not much else after that.

Alison Gopnik at UCBerkeley is studying learning in young children and I think (if I understand her “theory theory”) she theorizes that this kind of learning is present for children at a very early age, but that we tend to push kids in a different direction when they start school. http://psychology.berkeley.edu/people/alison-gopnik

I also wonder if Maria Montessori’s methods would be a way to foster transfer as an academic skill.

The image that comes to mind for me is that this innate or organic ability to transfer exists in little children like a tiny burning ember. The ember can be gently fanned and nurtured into a fire, or too strong a wind can extinguish the ember altogether. My gut tells me that the dominant education methods employed in most public schools fall into the latter category – winds so strong that they extinguish the ember.

It’s certainly true that young children have the ability to consider very disparate scenarios within the same framework. Not sure that this indicates the ability to transfer (in the sense of solving a problem using a concept from a different realm) so much as the willingness to!

It’s not even clear to me what it would mean to say, “I want kids to be able to transfer this strategy to a new context they know nothing about.” What would that look like? I don’t even know how to make sense of it.

If I understand correctly, one would not expect kids to be able to transfer a strategy to a new context that they know nothing about. If you know nothing about a new context, no strategy will make sense for you. Rather, the idea is that kids (or adults) can learn to use a familiar strategy in a different context that they do know something about, and in which they are facing a problem that at some level shares features with a problem that they have already solved in another realm.

Right, that’s my understanding also. So I’m always sort of confused when somebody expects some sort of shortcut, as if kids could think really critically about, say, tumors and rays without knowing anything about tumors or rays, if only they had the right habits of mind.

Bingo. As Dan Willingham states, you can’t think critically about a topic you don’t have any background knowledge about. I’m guessing that (in the example you cited above), the college students were supposed to know something about radiation and the way it can be targeted, but clearly they did not know enough. But even if they knew a lot about radiation, not every student would be creative (and visually-minded) enough to use the visual analogy of soldiers taking many different roads from different directions because of the triggering effect of too much weight, and basically transforming that paradigm to a visually similar conceptualization of bringing in a total radiation load from several directions NOT because of the effects of physical compression (which is in play in the military example) but because of the principle of tissue destruction by radiation.

Back to this one again. I am trying to understand this one before I retire.

I have done (and continue to do) a great deal of research on this one. I have a couple of issues on which I would appreciate your thoughts.

The first is your disinction between teaching the strategies and presentation of the contexts. You say…..

‘In other words, the question isn’t “How should teachers present the strategies more effectively?” so much as “How should teachers present additional contexts more effectively?”’

I am forming the view that the most important skill is the application of the idea/concept/procedure in unfamiliar contexts. By definition I will not be able to teach unfamiliar contexts or they will be familiar. The learner/thinker must be familiar with the “strategy”. Dan Willingham talks about deep structure.

When you suggest that teachers are wrong to suggest that learners do not really understand the application of the strategy (I prefer principle) I think this may be in error. It makes no difference how many contexts I present to learners. They must be able to identify that the strategy will work even when the surface structure of the problems are different i.e. not like one I have seen before or unfamiliar.

I see my task as explaining the strategy, including how the strategy works and the nature of the context which makes the strategy a suitable one. It is the practice of applying the strategy to problems that enables the learner to construct the knowledge they need to be able to apply in unfamiliar situations. I can surely teach contexts which will allow the use of the strategy in familiar (similar) contexts.

The learner “understands” the strategy when they are able to understand that the characteristics of the unfamiliar problem are suitable for the use of the strategy. I see application of the strategy as simply further practice which improves understanding of the strategy.

The second worry I have is about the issue of deep structure and mastery. Another subject that Dan Willingham explains well and has indeed given me some additional reading about.

There is much talk about chess players and mastery, about 10 years and 1000’s of hours. There is much talk of automatisation of procedures into declarative memory (if I understand correctly) that will allow deep structures to be recognised/recalled by experts. Dan Willingham talks about school kids not beinjg able to think like scientists as they are not experts.

Most of the learners I teach, do not become experts. There isn’t time etc and therefore they do not reach the point where they can recognise deep structures (unless someone can point me to reading that shows the opposite).

On the road to expertise learners use strategies that may be used to address problems even without deep structures. Most problems are therefore shallow structure and most problems are unfamiliar. I do not have deep structure to fall back on. I will teach the strategy and it’s characteristics and how to transfer to shallow problems using a variety of simple strategies perhaps.

I am starting to form the view that what we teach as ‘critical thinking skills”/”cognitive skills” is exactly this for most learners. Trying to find ways that novices can use to solve problems when they cannot use deep structure principles.

We do this by explaining the principle, applying the principle to familiar problems (similar surface structures) and then extending to different surface structures. With more practice we become more skilled. We understand the principle (strategy) more fully and more contexts become familiar in memory.

I might suggest that it is creativity that allows me to transfer the principle to unfamiliar problem structures.

So I am sort of disagreeing with your view that the issue isn’t that the learner doesn’t understand the principle and further that more contexts improves understanding of the principle.

Any reflections that might help me with my understanding.

Regards

ps…you say

“So I’m always sort of confused when somebody expects some sort of shortcut, as if kids could think really critically about, say, tumors and rays without knowing anything about tumors or rays, if only they had the right habits of mind.”

For me the issue is not whether habits of mind can help with unfamiliar surface structures, it is whether, given the information in the example is whether perhaps I can in fact see the appropriateness of the approach even if I am not an expert and am not armed armed with knowledge of the deep structure.

Maybe I can simply solve the problem of the tumour without transfer and without knowledge of the deep structure.

I understand the impulse to “see my task as explaining the strategy, including how the strategy works and the nature of the context which makes the strategy a suitable one”. Unfortunately, the evidence suggests that that’s not the way strategies work.

Instead, problem-solvers typically don’t recognize the deep structure of a problem because they don’t have knowledge about the details of the problem.

One way to think about it is this: What would it mean to say that a student “Doesn’t understand the dispersal/convergence strategy” if the student is able to apply that strategy to familiar contexts?

Suppose that we ran the experiment 100 years ago – before the invention of lasers – and found that people were able to successfully apply the dispersal/convergence strategy to other various problems (e.g., invading armies, large parties crossing bridges, etc.). In fact, imagine that there are some subjects who are able to successfully apply the strategy in every context that we offer them. (Again, we don’t offer the laser/tumor situation, because lasers don’t exist.)

Would we say in that situation that the highest-performing subjects understand the strategy? I would say, “yes”. Granted, if we put them in a time machine and brought them to today and then asked them the laser question, they’d probably be stumped. But would it make sense to say they were stumped *because they don’t understand the strategy*? I don’t think so. They’re stumped because they don’t know anything about lasers.

We shouldn’t let ourselves be biased by the fact that the experiment above included only two contexts – armies and lasers – and that subjects were thoroughly stumped on the only transfer task. In reality, subjects probably apply those strategies very frequently to solve relatively mundane and familiar problems. In other words, they demonstrate considerable understanding of the strategy on a day-to-day basis.

We also shouldn’t take too literally the expert/novice distinction. It’s a sliding scale, and being relatively more expert in an area is what makes one relatively more capable of solving problems in that area.

Also, you say, “the issue is not whether habits of mind can help with unfamiliar surface structures, it is whether, given the information in the example is whether perhaps I can in fact see the appropriateness of the approach even if I am not an expert and am not armed with knowledge of the deep structure”.

Again, that would be nice, but – almost by definition – knowledge of the deep structure is required to recognize that a strategy is relevant. The point is precisely that the surface features of problems vary in ways that are irrelevant to the general strategy. So by definition there’s no way to use the surface features of a problem to identify the best way to solve it.

So the point with the armies and lasers is that the surface features of the problem are different, and that people who don’t understand lasers won’t be able to see how the problems are similar at a deeper level.

(I’m actually not crazy about the surface/deep distinction, but it seems to be pretty commonly used this way, so it is what it is.)

I think part of the issue here is that you’re begging the question about whether general problem solving strategies can help students solve very diverse problems. As they state here:

There are basically no randomized, well-controlled studies indicating that instruction in such general strategies works.

I’m not even sure why we’d think such strategies *might* be effective. For example: Can you tell a plausible story about how somebody who doesn’t know anything about lasers would be able to transfer the dispersal/convergence strategy from the armies context to the laser context using only surface features of the problem?

I can’t come up with such a story, and am doubtful it’s possible to do so.